Chavance M, Escolano S
INSERM, CESP, Centre de recherche en Épidémiologie et Santé des Populations, Villejuif, France
INSERM, CESP, Centre de recherche en Épidémiologie et Santé des Populations, Villejuif, France.
Stat Methods Med Res. 2016 Apr;25(2):630-43. doi: 10.1177/0962280212462859. Epub 2012 Oct 14.
When fitting marginal models to correlated outcomes, the so-called sandwich variance is commonly used. However, this is not the case when fitting mixed models. Using two data sets, we illustrate the problems that can be encountered. We show that the differences or the ratios between the naive and sandwich standard deviations of the fixed effects estimators provide convenient means of assessing the fit of the model, as both are consistent when the covariance structure is correctly specified, but only the latter is when that structure is misspecified. When the number of statistical units is not too small, the sandwich formula correctly estimates the variance of the fixed effects estimator even if the random effects are misspecified, and it can be used in a diagnostic tool for assessing the misspecification of the random effects. A simple comparison with the naive variance is sufficient and we propose considering a ratio of the naive and sandwich standard deviation out of the [3/4; 4/3] interval as signaling a risk of erroneous inference due to a model misspecification. We strongly advocate broader use of the sandwich variance for statistical inference about the fixed effects in mixed models.
在对相关结果拟合边际模型时，通常会使用所谓的三明治方差。然而，在拟合混合模型时情况并非如此。我们使用两个数据集来说明可能遇到的问题。我们表明，固定效应估计量的朴素标准差与三明治标准差之间的差异或比率提供了评估模型拟合度的便捷方法，因为当协方差结构正确指定时两者都是一致的，但只有后者在结构指定错误时才是一致的。当统计单位数量不太小的时候，即使随机效应指定错误，三明治公式也能正确估计固定效应估计量的方差，并且它可以用作评估随机效应指定错误的诊断工具。与朴素方差进行简单比较就足够了，我们建议将朴素标准差与三明治标准差的比率超出[3/4; 4/3]区间视为由于模型指定错误而导致错误推断风险的信号。我们强烈主张更广泛地使用三明治方差来对混合模型中的固定效应进行统计推断。
